Which set of numbers is correctly ordered from least to greatest?

A. [tex]\(\frac{24 \pi}{5}, \frac{63}{4} \cdot 15.758\)[/tex]
B. [tex]\(\frac{24 \pi}{5}, 15.758, \frac{63}{4}\)[/tex]
C. [tex]\(15.758, \frac{63}{4}, \frac{24 \pi}{5}\)[/tex]
D. [tex]\(\frac{63}{4}, 15.758, \frac{24 \pi}{5}\)[/tex]



Answer :

To determine the correct order of the given numbers from least to greatest, we will first examine and compare the given values:

1. [tex]\(\frac{24 \pi}{5}\)[/tex]
2. [tex]\(\frac{63}{4} \cdot 15.758\)[/tex]
3. [tex]\(15.758\)[/tex]
4. [tex]\(\frac{63}{4}\)[/tex]

We need the numerical values of each term:

1. [tex]\(\frac{24 \pi}{5} \approx 15.079644737231007\)[/tex]
2. [tex]\(\frac{63}{4} \cdot 15.758 \approx 248.18849999999998\)[/tex]
3. [tex]\(15.758\)[/tex]
4. [tex]\(\frac{63}{4} \approx 15.75\)[/tex]

Now let's list these values together:

- [tex]\(\frac{24 \pi}{5} \approx 15.079644737231007\)[/tex]
- [tex]\(\frac{63}{4} \cdot 15.758 \approx 248.18849999999998\)[/tex]
- [tex]\(15.758\)[/tex]
- [tex]\(\frac{63}{4} \approx 15.75\)[/tex]

To order them from least to greatest:

1. [tex]\(\frac{24 \pi}{5} \approx 15.079644737231007\)[/tex]
2. [tex]\(\frac{63}{4} \approx 15.75\)[/tex]
3. [tex]\(15.758\)[/tex]
4. [tex]\(\frac{63}{4} \cdot 15.758 \approx 248.18849999999998\)[/tex]

Therefore, the numbers ordered from least to greatest are:

[tex]\[\frac{24 \pi}{5}, \frac{63}{4}, 15.758, \frac{63}{4} \cdot 15.758\][/tex]

Which corresponds to the original statement:

[tex]\[ \frac{24 \pi}{5}, \frac{63}{4}, 15.758, \frac{63}{4} \cdot 15.758 \][/tex]

So, the correct ordering from least to greatest is:

[tex]\[ \boxed{\frac{24 \pi}{5}, 15.758, \frac{63}{4} \cdot 15.758} \][/tex]

However, recognizing this isn't in your stated options. Reviewing and interpreting one of the provided options correctly links:

the position that fits is:

[tex]\[ \boxed{\frac{24 \pi}{5}, 15.758, \frac{63}{4}} \][/tex]

rather than numeric column, it should be meaningful:

This combination matching the sequentially correct ordering is:

\[
\boxed{\frac{63}{4}, 15.758, \frac{24 \pi}{5}}
}.